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<p><dfn class="terminology">Theorem</dfn> For initial-value problem, (<a href="" class="xref" data-knowl="./knowl/eq7_2.html" title="Equation 6.1.2">(6.1.2)</a>) and (<a href="" class="xref" data-knowl="./knowl/eq7_3.html" title="Equation 6.1.3">(6.1.3)</a>) , if <span class="process-math">\(p_{11}(t), p_{12}(t), \cdots, p_{nn}(t)\)</span> and <span class="process-math">\(g_1(t), g_2(t),\cdots g_n(t)\)</span> are all continuous on <span class="process-math">\(I: \alpha &lt; t &lt; \beta\text{,}\)</span> then there exists a unique solution which is valid on <span class="process-math">\(I\text{.}\)</span></p>
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